Linked Questions
13 questions linked to/from Difficulties with bra-ket notation
7
votes
6
answers
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Is H=H* sloppy notation or really just incorrect, for Hermitian operators?
I saw it in this pdf, where they state that
$P=P^\dagger$ and thus $P$ is hermitian.
I find this notation confusing, because an operator A is Hermitian if
$\langle \Psi | A \Psi \rangle=\langle A \...
- 1,062
11
votes
1
answer
4k
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Existence of adjoint of an antilinear operator, time reversal
The time reversal operator $T$ is an antiunitary operator, and I saw $T^\dagger$ in many places (for example when some guy is doing a "time reversal" $THT^\dagger$), but I wonder if there is a well-...
- 1,071
5
votes
3
answers
1k
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Dirac notation - specific acting orientation for operators
I have this doubt:
Imagine two operators $A$ and $B$ and the state $\psi$.
I know that the following statement is true:
$$\langle\psi| A|\psi\rangle^*=\langle\psi| A^\dagger|\psi\rangle$$
But is ...
- 1,032
4
votes
2
answers
2k
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Adjoint of a Wave Function
Why is the adjoint of a function simply it's complex conjugate? Normally with a vector we consider the adjoint to be the transpose (And the conjugate? I don't know why), so does this concept carry ...
user24082
2
votes
3
answers
1k
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How do you show that momentum is hermitian in Dirac notation?
I am trying to prove that momentum operator $\bf{\hat{p}}$ is hermitian. I know how to prove it in the $\bf{x}$ representation integrating by parts and using the fact that $\lim_{r \rightarrow \infty} ...
- 1,064
0
votes
1
answer
952
views
What is the adjoint of a ket-bra?
Let $T$ be a linear operator, then we can consider the rank-one operator
$$\vert Tx \rangle \langle y \vert.$$
I am wondering what is its adjoint operator, is it
$$\vert y \rangle \langle T^*x \...
- 117
0
votes
2
answers
921
views
How to prove this identity for the complex conjugate of linear operator?
I want to prove the following identity:
$$\langle v|\Omega^{\dagger}|u\rangle = \langle u|\Omega | v \rangle^*$$
How should I go about this? I believe I can prove it when $\Omega$ is hermitian, but ...
0
votes
2
answers
207
views
Associative product of two Anti-Linear(/Unitary) Operator
An operator is said to be linear if it obeys the distributive law and commutes with the constant i.e.
$\hat{A}(a_1 |\psi_1\rangle + a_2|\psi_2\rangle)=a_1\hat{A}|\psi_1\rangle +a_2\hat{A}|\psi_2\...
- 119
-1
votes
1
answer
279
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Property of the adjoint operator in the array element
In Quantum Mechanics how can I prove this property?
$$<\psi|A^{\dagger} |\phi>=<\phi|A|\psi>^{*}$$
2
votes
1
answer
200
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Notation doubt - inner product
I have a notational problem, I know when you define bra and ket you are defining an inner product, but you can see it as an linear operation where the linear operators (bras) act on vectors (kets), ...
- 193
1
vote
2
answers
107
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Distributing operators inside of the bra and kets confusion
I'm reading Griffiths and he has this section where he states that $|\hat{Q}f\rangle$ is mathematical nonsense and that really we should write $\hat{Q}|f\rangle$, where the latter makes more sense to ...
- 111
0
votes
2
answers
119
views
Dirac expression derivation
In Quantum Mechanics, 2nd Edition by Davies & Betts on page 78 it states that there is a symmetry implied by the following Hermitian operator equation:
$${\displaystyle \int \phi^{*}(A \psi)d \,\...
user248988
0
votes
2
answers
80
views
Does an orthonormal basis imply hermiticity of operator?
I am confused as to what hermiticity of an operator means when given a basis set.
My course notes say that hermitian operators in Hilbert space stay unchanged under it's complex conjugate:
$$<n|A|m&...
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